扫一扫
关注中图网
官方微博
本类五星书更多>
-
>
宇宙、量子和人类心灵
-
>
(精)BBC地球故事系列-星际旅行
-
>
从一到无穷大
-
>
图说相对论(32开平装)
-
>
一本有趣又有料的化学书
-
>
刘薰宇的数学三书:原来数学可以这样学全3册
-
>
光学零件制造工艺学
GTM 79-遍历性理论引论 版权信息
- ISBN：7506260093
- 条形码：9787506260091 ; 978-7-5062-6009-1
- 装帧：暂无
- 册数：暂无
- 重量：暂无
- 所属分类：>>
GTM 79-遍历性理论引论 内容简介
in 1970 i gave a graduate course in ergodic theory at the university of maryland in college park, and these lectures were the basis of the springer lecture notes in mathematics volume 458 called "ergodic theory--introductory lectures" which was published in 1975. this volume is nowout of print, so i decided to revise and add to the contents of these notes. i have updated the earlier chapters and have added some new chapters on the ergodic theory of continuous transformations of compact metric spaces. in particular, i have included some material on topological pressure and equilibrium states. in recent years there have been some fascinating interactions of ergodic theory with differentiable dynamics, differential geometry,number theory, von neumann algebras, probability theory, statistical mechanics, and other topics. in chapter 10 1 have briefly described some of these and given references to some of the others. i hope that this book will give the reader enough foundation to tackle the research papers on ergodictheory and its applications.
GTM 79-遍历性理论引论 目录
chapter 0 preliminaries
0.1 introduction
0.2 measure spaces
0.3 integration
0.4 absolutely continuous measures and conditional expectations
0.5 function spaces
0.6 haar measure
0.7 character theory
0.8 endomorphisms of tori
0.9 perron-frobenius theory
0.10 topology
chapter 1 measure-preserving transformations
1.1 definition and examples
1.2 problems in ergodic theory
1.3 associated isometries
1.4 recurrence
1.5 ergodicity
1.6 the ergodic theorem
1.7 mixing
chapter 2 isomorphism, conjugacy, and spectral isomorphism
2.1 point maps and set maps
2.2 isomorphism of measure-preserving transformations
2.3 conjugacy of measure-preserving transformhtions
2.4 the isomorphism problem
2.5 spectral isomorphism
2.6 spectral invariants
chapter 3 measure-preserving transformations with discrete spectrum
3.1 eigenvalues and eigenfunctions
3.2 discrete spectrum
3.3 group rotations
chapter 4 entropy
4.1 partitions and subalgebras
4.2 entropy of a partition
4.3 conditional entropy
4.4 entropy of a measure-preserving transformation
4.5 properties orb t,a and h t
4.6 some methods for calculating h t
4.7 examples
4.8 how good an invariant is entropy
4.9 bernoulli automorphisms and kolmogorov automorphisms
4.10 the pinsker -algebra of a measure-preserving transformation
4.11 sequence entropy
4.12 non-invertible transformations
4.13 comments
chapter 5 topological dynamics
5.1 examples
5.2 minimality
5.3 the non-wandering set
5.4 topological transitivity
5.5 topological conjugacy and discrete spectrum
5.6 expansive homeomorphisms
chapter 6 invariant measures for continuous transformations
6.1 measures on metric spaces
6.2 invariant measures for continuous transformations
6.3 interpretation of ergodicity and mixing
6.4 relation of invariant measures to non-wandering sets, periodic points and topological transitivity
6.5 unique ergodicity
6.6 examples
chapter 7 topological entropy
7.1 definition using open covers
7.2 bowen's definition
7.3 calculation of topological entropy
chapter 8 relationship between topological entropy and measure-theoretic entropy
8.1 the entropy map
8.2 the variational principle
8.3 measures with maximal entropy
8.4 entropy of affine transformations
8.5 the distribution of periodic points
8.6 definition of measure-theoretic entropy using the metrics dn
chapter 9 topological pressure and its relationship with invariant measures
9.1 topological pressure
9.2 properties of pressure
9.3 the variational principle
9.4 pressure determines m x, t
9.5 equilibrium states
chapter 10 applications and other topics
10.1 the qualitative behaviour of diffeomorphisms
10.2 the subadditive ergodic theorem and the multiplicative ergodic theorem
10.3 quasi-invariant measures
10.4 other types of isomorphism
10.5 transformations of intervals
10.6 further reading
references
index
0.1 introduction
0.2 measure spaces
0.3 integration
0.4 absolutely continuous measures and conditional expectations
0.5 function spaces
0.6 haar measure
0.7 character theory
0.8 endomorphisms of tori
0.9 perron-frobenius theory
0.10 topology
chapter 1 measure-preserving transformations
1.1 definition and examples
1.2 problems in ergodic theory
1.3 associated isometries
1.4 recurrence
1.5 ergodicity
1.6 the ergodic theorem
1.7 mixing
chapter 2 isomorphism, conjugacy, and spectral isomorphism
2.1 point maps and set maps
2.2 isomorphism of measure-preserving transformations
2.3 conjugacy of measure-preserving transformhtions
2.4 the isomorphism problem
2.5 spectral isomorphism
2.6 spectral invariants
chapter 3 measure-preserving transformations with discrete spectrum
3.1 eigenvalues and eigenfunctions
3.2 discrete spectrum
3.3 group rotations
chapter 4 entropy
4.1 partitions and subalgebras
4.2 entropy of a partition
4.3 conditional entropy
4.4 entropy of a measure-preserving transformation
4.5 properties orb t,a and h t
4.6 some methods for calculating h t
4.7 examples
4.8 how good an invariant is entropy
4.9 bernoulli automorphisms and kolmogorov automorphisms
4.10 the pinsker -algebra of a measure-preserving transformation
4.11 sequence entropy
4.12 non-invertible transformations
4.13 comments
chapter 5 topological dynamics
5.1 examples
5.2 minimality
5.3 the non-wandering set
5.4 topological transitivity
5.5 topological conjugacy and discrete spectrum
5.6 expansive homeomorphisms
chapter 6 invariant measures for continuous transformations
6.1 measures on metric spaces
6.2 invariant measures for continuous transformations
6.3 interpretation of ergodicity and mixing
6.4 relation of invariant measures to non-wandering sets, periodic points and topological transitivity
6.5 unique ergodicity
6.6 examples
chapter 7 topological entropy
7.1 definition using open covers
7.2 bowen's definition
7.3 calculation of topological entropy
chapter 8 relationship between topological entropy and measure-theoretic entropy
8.1 the entropy map
8.2 the variational principle
8.3 measures with maximal entropy
8.4 entropy of affine transformations
8.5 the distribution of periodic points
8.6 definition of measure-theoretic entropy using the metrics dn
chapter 9 topological pressure and its relationship with invariant measures
9.1 topological pressure
9.2 properties of pressure
9.3 the variational principle
9.4 pressure determines m x, t
9.5 equilibrium states
chapter 10 applications and other topics
10.1 the qualitative behaviour of diffeomorphisms
10.2 the subadditive ergodic theorem and the multiplicative ergodic theorem
10.3 quasi-invariant measures
10.4 other types of isomorphism
10.5 transformations of intervals
10.6 further reading
references
index
展开全部
书友推荐
- >
推拿
推拿
¥12.2¥32.0 - >
巴金－再思录
巴金－再思录
¥15.6¥46.0 - >
伊索寓言-世界文学名著典藏-全译本
伊索寓言-世界文学名著典藏-全译本
¥6.1¥19.0 - >
苦雨斋序跋文-周作人自编集
苦雨斋序跋文-周作人自编集
¥6.9¥16.0 - >
随园食单
随园食单
¥20.6¥48.0 - >
姑妈的宝刀
姑妈的宝刀
¥12.9¥30.0 - >
唐代进士录
唐代进士录
¥17.1¥39.8 - >
二体千字文
二体千字文
¥14.0¥40.0
本类畅销
-
矩阵论
¥9.5¥28 -
高等代数专题研究学习指导书
¥5.9¥12 -
2022图书×抽奖盲袋
¥9.9¥25 -
2023读书月阅读盲盒——天黑，闭眼，刀谁？
¥42.3¥158 -
-
2022读者节纪念徽章-三星会员专属
¥45¥45.6
